Comparison & Regression Questions Use the following scenario to answer questions

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Comparison & Regression Questions

Use the following scenario to answer questions 1 and 2.

A university is interested in the holistic wellness of students attending the institution. Given extensive wellness programming that occurs each year, the university believes students’ wellness improves each year they are enrolled. In order to determine if this is true, the university took a wellness measurement on students (wellness score) and compared by classification (freshman, sophomore, junior, senior) to determine if there are differences. The resulting 1 X 4 ANOVA resulted in a rejection of the HO. As such, the university must now determine where the differences occurred.

List the HO for each pairwise post hoc comparison.

How will you know from the pairwise post hoc comparisons where the difference(s) in the levels occur?

When would you perform a priori planned comparisons instead of pairwise omnibus post hoc comparisons?

What advantage does a priori planned comparisons have over pairwise omnibus post hoc comparisons?

Use the following scenario to answer questions 5 –8

A university admissions officer wants to impress his/her supervisor with newly acquired statistical knowledge. The admissions officer believes he/she can use high school GPA, high school class rank, SAT score, and ACT score to predict the first semester GPA of entering freshman students. The admissions officer decides to utilize multiple regression.

What is the criterion variable?

What are the predictor variables?

What is the unstandardized regression equation?

If the resulting analysis yields a coefficient of determination of r2=.47, what do we know?

Explanation / Answer

1. The list of Null Hypothesis (H0) for pairwise post hoc comparison are:

H01:There is no significance difference between the mean wellness scores among freshman and sophomore

H02:There is no significance difference between the mean wellness scores among freshman and junior

H03:There is no significance difference between the mean wellness scores among freshman and senior

H04:There is no significance difference between the mean wellness scores among sophomore and junior

H05:There is no significance difference between the mean wellness scores among sophomore and senior

H06:There is no significance difference between the mean wellness scores among junior and senior

2. If the significance value(or p-value) of one comparison say A and B is less than level of significance (%) we say that the means of these two groups differ significantly.

3. Priori planned comparisons are performed when only a few comparisons based on scientific goals are required, that is when we want to compare A with B and B with C and that’s it. That means we are not interested in comparing other pair like A with C. Whereas pairwise omnibus post hoc comparisons are used to determine which mean differs from other means (compares all possible pairwise means) after obtaining a significant omnibus test (it means that among the tested means, at least two of the means are significantly different ).

4. We seek to compare only the groups of interest based on evidence of specific hypothesis and don’t have to perform ANOVA and then compare all groups to each other to see where the difference lies.

5. First semester GPA of entering freshman students(Y).

6. High school GPA(X1), high school class rank(X2), SAT score(X3), and ACT score(X4).

7. Y=a1X1+a2X2+a3X3+a4X4+a5 ; where a1,a2,a3 and a4 are unstandardized coefficients, that is an increase in X1 by one unit is associated with an increase of a1 units in Y keeping the other coefficients constant. Similarly for X2,X3 and X4

8. 47% of variability in the dependent variable or criterion variable (First semester GPA of entering freshman students) is predicted by the independent variables or predicted variables (High school GPA, high school class rank, SAT score, and ACT score)

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